Question

consider the given statement.
some employees in the office have a desk.
for each statement below, determine whether it is a negation of the given statement.
all employees in the office have a desk.
none of the employees in the office have a desk.
every employee in the office has a desk.
some employees in the office do not have a desk.

Explanation:

The original statement "Some employees in the office have a desk" is an existential statement (there exists at least one employee with a desk). The logical negation of an existential statement "Some A are B" is the universal statement "No A are B" (or "None of the A are B"), meaning there are zero employees with a desk.

• "All/Every employee has a desk" is a different universal statement, not the negation.
• "Some employees do not have a desk" is the contrary of the original statement, not its negation, as both the original and this statement can be true at the same time.

Answer:

1. All employees in the office have a desk. → No
2. None of the employees in the office have a desk. → Yes
3. Every employee in the office has a desk. → No
4. Some employees in the office do not have a desk. → No